here are the pics i promised
as you can see the bottom roof needs to tie into the top two pitches and eliminate the troughing
we would like to level all floors and entrances with the main house
considering the addition floor sits level with the garage entrance but is about 6 inches lower than the house entrance, we will need to raise the garage door lintel
overall we would like about a foot added to the addition height maybe more depending on the doorway lift
the addition is in red on the floor plan

Is the outside wall sitting on a foundation or just built on top of a patio deck. If you have a foundation, you would build the floor and stand new walls to match the house,6" high floor over concrete may be a problem. I wouldn't do anything without footings and foundation. You may want to take the old patio out.
If you are leaving the wall between the rooms in place your local truss company could build add on trusses and they would tell you what and how much of your old roof would have to be removed. The chimney will have to made higher.

I guess you could design some sort of flat roof, I just thought you would be adding to what you have witch would raise the peak. You could do a lower slope from the the peak that you have. When I first looked at this I thought this was the front of the house, but as it is the back I would just go with the low slope so it didn't show from the front.